The Exponential Function Learns To Wear PolesThis scene uses the classical Padé rational approximation of the exponential function. Instead of drawing arbitrary roots and poles, we start withRₙ(ζ) = Pₙ(ζ) / Pₙ(−ζ),where Pₙ is the diagonal Padé numerator for eᶻ. The roots of Pₙ become the zeros of the rational function, and the roots of Pₙ(−ζ) become its poles.Then the complex plane is gently warped by ζ = λ(t)eⁱᶿ(t)(z + c₂(t)z² + c₃(t)z³ + s(t))The visible pellets are the actual preimages of the